A device thus constructed is used notably for the classification of objects, that is to say for the recognition of objects: it concerns, for example the recognition of shapes and notably the recognition of characters.
Such a method of construction is known from the document "A neural model for categories learning" by Douglas L. Reilly et al., published in "Biological Cybernetics", No. 45, 35-41 (1982). The network is constructed by incremental learning and the decision to determine the class is taken on the basis of a variable-threshold function which defines a domination volume around the samples in a hyperspace.
The more or less random introduction of the samples can nevertheless have the effect that, in order to achieve sufficient reliability, the number of hidden neurons reaches a value which is higher than that which would be obtained for optimum definition of these neurons, resulting in a longer calculation time during use of the network. The invention has for its object to provide a network which, constructed by means of this method, is very fast during use.
To this end, in accordance with the invention, groups of neurons with a neuron which is representative of each group are defined according to the introduction of hidden neurons while searching, for each of the neurons introduced, whether it forms part of a previously defined group, in which case it is incorporated therein, whereas if it does not form part of any previously defined group, a new group is formed for which it constitutes the representative neuron, the first neuron introduced thus having been defined as being representative of a first group.
According to this method, a neuron is preferably considered to form part of a given group if the distance between the reference point associated with this neuron and the reference point associated with the neuron which is representative of the relevant group is smaller than a given distance.
In a further embodiment, the groups in question being considered to be of a first level, at least one second given distance is defined which is greater than the first distance and on the basis of which at least second groups of a second level are defined in the course of the same process as the groups of the first level.
When two hidden neurons corresponding to two learning samples have representative points whose coordinates neighbour one another, without said samples belonging to the same class, an inhibitory connection of negative weight is advantageously inserted between the hidden neuron corresponding to one of the samples and the output neuron corresponding to the class of the other sample.
The reliability of the classification results is thus improved.
When the activation of the hidden neurons is a predetermined, nonadjustable function of the distance between the reference points, it may occur that the sensitivity of the device to differences between given samples is too low for correctly distinguishing the samples.
In order to solve this problem, a supplementary hidden neuron which corresponds to a learning sample is preferably inserted with a connection to the corresponding output neuron if for this sample, presented as an object to be classified, an output neuron is effectively activated for the desired class, but the difference between the activity of the output neuron which has the highest activation level, the output neuron which has the highest activation level but one is below a given threshold.
For a given organization of the network, the choice of the activation values for the hidden neurons and the selection rule determining the class as a function of the activation of the output neurons has an important impact on the performance. In the document cited above, the use of an activation function for the hidden neurons which is zero below the threshold does not allow for a progressive integration of the effect of "remote" learning samples, and the use of "binary" (all or nothing) neurons in the output layer does not allow for motivated decisions to be taken. Moreover, it is not possible to manage a situation in which two output neurons are simultaneously active.
Therefore, the method is more advantageously applied in a device in which the activation of a hidden neuron is a decreasing, e.g., an inverse, function of the geometrical distance in the hyperspace between the reference point associated with the hidden neuron and the point representing the input vector, in which activation of an output neuron is a function of an input threshold, and for which the class indicated as a result is that which corresponds to the most activated output neuron, subject to the condition that the difference between the activity of the latter and that of the output neuron whose activation is strongest after that of the most activated output neuron exceeds a given value.
This has inter alia the advantage that not only a winner can be proposed, but also a list of winners in decreasing order of probability, this is an important advantage for character recognition where said list can subsequently be used to correct errors on the basis of a dictionary.
A device of this kind in which the hidden neurons and their associated reference points have been determined and the hidden neurons have been subdivided into groups, each group comprising a neuron which is representative of the group, in conformity with the method in accordance with the invention, preferably comprises means for operating, upon presentation of a sample to be classified, only the representative hidden neurons during a first period, that is to say for all groups, and to determine which neuron provides the highest activation level, followed by operating, during a second period, all hidden neurons of the group or a few groups whose representative neuron (neurons) has (have) provided the highest activation level during the first period.
When several group levels have been defined, the device preferably comprises means for operating, upon presentation of a sample to be classified, only the hidden neurons representative of the groups of an n.sup.th level during a first period, and for determining which neuron provides the highest activation level, means for operating, during a second period, only the hidden neurons representative of the groups of the (n-1).sup.th level contained in the group of the n.sup.th level whose representative neuron provided the highest activation level during the first period, and for determining which neuron provides the highest activation level, and so on until the first level is reached.
This device is also characterized in that, for each of the hidden neurons, the activation is calculated on the basis of the distance in the hyperspace between a reference point associated with this hidden neuron and the point representing the input vector, and to this end it comprises means for determining the activation of a hidden neuron having the index "i" e.g. by way of the formula ##EQU1## in which W.sub.ki represents the K coordinates of the sample having triggered the formation of the neuron "i", .sigma..sub.i is an adjustable coefficient associated with the neuron "i", X.sub.k represents the K coordinates of an input vector to be classified, n is an integer, for example equal to two, and the function "f" is a function which increases as its argument tends towards zero, an output neuron being such that it is activated only beyond a given activation threshold of a hidden neuron, there being provided means for indicating as a result the class which corresponds to the neuron of the output layer providing the highest activation level, subject to the condition that the difference between the activity of the latter and that of the output neuron whose activation level is highest but one exceeds a given value.
Preferably, this device comprises an inhibitory connection of negative weight between a hidden neuron corresponding to a sample and an output neuron corresponding to the class of another sample in the case where two hidden neurons corresponding to two learning samples have representative points whose coordinates neighbour one another, without said samples belonging to the same class.